Question

Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 43 days and a standard deviation of 10.1 days. Find the probability that a simple random sample of 25 protozoa will have a mean life expectancy of 46 or more days.

Answer 1

Answer: 0.0688

Step-by-step explanation:

Given : Current research indicates that the distribution of the life expectancies of a certain protozoan is normal with a mean of 43 days and a standard deviation of 10.1 days.

i.e. $\mu=43$  and $\sigma= 10.1$

Let x represents the  life expectancies of a certain protozoan.

Sample size : n= 25

The probability that a simple random sample of 25 protozoa will have a mean life expectancy of 46 or more days. :-

$P(x\geq46)=1-P(x<46)\\\\=1-P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{46-43}{\dfrac{10.1}{\sqrt{25}}})\\\\ =1-P(z<1.485 )$

$=1-0.9312=0.0688$   [using z-value table]

Hence, the required probability = 0.0688